نبذة مختصرة : The study of triangulations on manifolds is closely related to understanding the three-dimensional homology cobordism group. We review here what is known about this group, with an emphasis on the local equivalence methods coming from Pin(2)- equivariant Seiberg-Witten Floer spectra and involutive Heegaard Floer homology.
14 pages. Written for the Proceedings of the ICM 2018. v2: Fixed definition of \Theta^n_Z on p.2
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